"Flight paths in the Southern Hemisphere" Would you care to elaborate? The flights in the Southern Hemisphere directly contradict the idea of a flat earth, I'm curious why you think they don't. For example, Air New Zealand operates a non-stop from Buenos Aires to Aukland New Zealand. It takes a little over 13 hours to go west, and under 12 hours to return eastbound. Now let's look to the northern hemisphere. Flight times from Los Angeles to and from Beijing are pretty close to the same: 12h50m going west, 12h exactly going east. Let's look at those two routes on the 'flat earth map' (which I put in quotation marks because there IS no one 'flat earth map' they can agree on, because each proposed map has flaws). It is quite obvious that the route on a flat earth between Buenos Aires and Aukland is twice (or more) the distance of the LA to Beijing route, do you really think the airlines run their planes at double (or more) the airspeed? Especially when you look at the flight right along side it, from Dallas to/from Buenos Aires, that takes 11 hours? And besides all that, have you seen a map of Australia? Does it look like that?
"Vanishing point of ships on the horizon" I can tell you with absolute certainty, gained from my own personal experience as a sailor in the US Navy, that ships do not become visible again once they go over the horizon. The objects that can be resolved again with telescopes or binoculars after becoming indistinct to the naked eye have not gone over the horizon, they've merely gone far enough away that they become too small for the eye to resolve against the background. In the Navy I have used bigger optics than most people ever see in their lives, like this for example:
"Lack of photographic evidence of a globe" is only true if you deny the existence of spaceflight. Do not be fooled by all the noise about "why can't I see the curve". The earth is enormous. Far FAR too big for you to be able to see any curvature at the tiny, miniscule human scales we operate at.
"Sun and moon being visually the exact same size" This is a cosmic coincidence, it's true. The flat earth side wants you to think such a coincidence is impossible, but it really is no more amazing than the coincidence required by the flat earth: that these two very different bodies actually ARE (almost) the exact same size, and (almost) the exact same distance, and yet they never bump into each other, not once?
ETC.
"Are there other questions I should challenge" Yes, OMG there is so much! How does the sun (and moon) set if it never actually goes below the horizon? How does the sun (and moon) appear to be the same size at noon when they're close to you as it does at sunrise/sunset when they are several multiples of their noon distance away? Telescopes large and small are mounted on equatorial mounts, with their rotation axis tilted to match the round earth's axis, and this actually does allow the scope to remain pointed at the same object in the sky: how does that work, if the earth is flat? Stars in the northern hemisphere appear to rotate in the sky counterclockwise around a fixed point in the heavens, but in the southern hemisphere they rotate CLOCKWISE around a different fixed point. How could that be, on a flat earth? I could go on, but maybe you would like to
read what you find here as a starting point. Several of those are my contributions, along with a few other of us core round earth adherents.